states that the price changes based on how many units have sold?
uniswap uses the same algorithm. The pool owners will take a fee on every trade, but they have no control over the end state, for when they want to withdraw their money. They may get more of the token and less bch at the end, or the other way around and lose money as the result.
Sorr if I don’t understand your question and I’m telling you something you already know, but in the case of an AMM dex, “LP” is two tokens, balanced, any deposit of one token results in the withdrawal of the other token, the “price” is based on the ratio of the two tokens, and the ratio changes dynamically; the price is calculated based on the size of the new deposit, not the current ratio.
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